I hope you at least left the gut pile on your side of the fence?
I'd simply apologize for trespassing and send them a nice gift as a piece offering, go plow there driveway out, do something neighborly..You screwed up, you're a schmuck, own up to it. She thinks it's a big deal, , you have to respect that. Offer her the deer in question, promise you wont do it again, make a deal that a phone call either way will get cooperation in the future even if that means splitting the meat. If sucking up nicely doesn't work, you can always build a bigger fence, but it's harder to tear down fences than to build them. MUCH HARDER. You started on the wrong foot so you're going to have to take the extra step to set things right. Once you get things calmed down then maybe suggest some sort of QDM cooperation or if it goes the other way, live with the fact that you can not cross the line. I've been hunting public and most of the deer I've seen were off limits. That's hunting. Shooting a deer and keeping it from crossing property lines unfortunately is also apart of hunting. Been there many times with my bow.
I only know this from experience because one day I was the schmuk who did the same thing. Wasn't a big deal til someone else had a problem with it. If roles were reversed, treat thy neighbor as you would have them treat you and in this case treat thy neighbor as they wish to be treated. If she doesn't want to see you retrieve game, don't let her see you retrieve game. If that means go by night, be prepared to pay the price. If you can not afford the price of getting caught, don't do it. It may not be the price of just one ticket, DNR never write just 1 ticket. You start a fued and everyone looses. Make friends, be nice, you'll get much further.
American by birth, hunter by choice.